Fair matchings and related problems
Paper in proceedings, 2013

© Chien-Chung Huang, Telikepalli Kavitha, Kurt Mehlhorn, and Dimitrios Michail. Let G = (A [ B,E) be a bipartite graph, where every vertex ranks its neighbors in an order of preference (with ties allowed) and let r be the worst rank used. A matching M is fair in G if it has maximum cardinality, subject to this, M matches the minimum number of vertices to rank r neighbors, subject to that, M matches the minimum number of vertices to rank (r-1) neighbors, and so on. We show an efficient combinatorial algorithm based on LP duality to compute a fair matching in G. We also show a scaling based algorithm for the fair b-matching problem. Our two algorithms can be extended to solve other profile-based matching problems. In designing our combinatorial algorithm, we show how to solve a generalized version of the minimum weighted vertex cover problem in bipartite graphs, using a single-source shortest paths computation - this can be of independent interest.

Matching with Preferences

Complementary Slackness

Bipartite Vertex Cover

Fairness and Rank-Maximality

Linear Programming Duality


Chien-Chung Huang

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

T. Kavitha

K. Mehlhorn

D. Michail

Leibniz International Proceedings in Informatics, LIPIcs: 33rd International Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2013; Guwahati; India; 12 December 2013 through 14 December 2013

1868-8969 (ISSN)

Vol. 24 339-350

Subject Categories

Computer Science





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